Thank you. I was explaining to my friend why in "order of operations" that multiplication and division were interchangeable same with addition and subtraction. And when i said "because basically theyre the same thing" she looked at me as if i was crazy 😂
@@savazeroa try solving 5+2*6 solely going left to right without using order of operations. That's how many eggs I collected from the chooks over the past 3 days, so there is a correct answer: 17
I am so glad that Im getting an explanation for complex math, my teachers all basically taught me was "this is how you use them because this is how they are used" but now why they are used that way or what they are, and for me to learn I have to actually understand something at a fundamental level
this is what I'm saying. for real many teachers teach by just saying " this is just how it is" which I think drags out the fun and also much of the basic human crave and understanding of why something is which in return make it easier to learn.
A future original 3B1B in the making, keep up the great work and amazing videos. Would love to see longer videos if it meant minimizing holes and gaps. Thank you for your work!
@@Shadoxite from my other commentary (only watched a few minutes and stopped): "Tetration is useful in combinatorics and pure mathematics is not about applications. Applications are easy and they will always show up sooner or later. Root and 1/p power are not the same operations. Only if you match the domains specifically and pick a certain root, you could somewhat bring them together say for R+. They are two very different beasts if you properly consider complex numbers. Why are you confusing people if you don't understand the basics yourself?"
I always find it so odd that people struggle so much with algebra. Probably a result of it being taught way too late, as substitution is so basic that it really should just be taught around the same time as multiplication (and should be followed within a year or two by parentheses and factorisation, as they're another one people tend to struggle with due to how late they're taught.)
I see people struggling with Fractions, it's so easy, it's literally just division and people struggle with it, in my opinion they should only teach fractions and avoid pure division as much as possible, because in the future(High school) these people won't use "÷" anymore and will only use fraction.
@@reclaimer2019 you could probably teach ÷ when teaching other alternative notations like *, ^, and ↑↑↑ and just teach them like you would alternative characters in English like @, &, etc. Though you can always just teach both division and fraction notation simultaneously as different was of writing it, as ÷ is really important for factorisation, as 1/x(2+3) [2*(1/x)+3*(1/x)] and 1÷x(2+3) [1÷(2x+3x)] aren't the same thing [x=1, 1/1(2+3)=5, 1÷(2*1+3*1)=1/5]. You Can get around this with 1/(x(2+3)) or a long fraction sign that I don't feel like looking for the unicode for, but a division sign does the job just fine too.
@@reclaimer2019they should be taught that these are equal, also, the notation for a single line equation can get very messy, but it makes absurd sense. Like how 1/1+1 is different than 1/(1+1), but some people seem to not be able to recognize this.
People struggle with algebra due to the fact it makes no sense. This is because algebra in Western countries isn't taught systematically but with an adhoc approach. When we were going over equations we never went over what operations you can do to them. Also parentheses aren't explained well usually. For example something like this 5+(5-4) would be "incorrect" to solve as 5+5-4=6 even though the parenthesis in this case do nothing.
@@SbF6H the thing with these equations is that, if you dont know what it represents, its very difficult to reverse engineer what it represents even if you know the notation unlike some simpler equations. i personally didnt know it but its pretty easy to understand.
Got to hand it to you mate, although i knew these concepts beforehand, the visualization and most importantly your explanations were amazing, very underrated video, amazingly put
Merry Christmas! I'm a freshman taking AP CSP and this helped me a lot. I have no prior experience in calculus, so this really helped me get a grasp on frequency space to time space conversions and vice versa. It would be incredibly helpful if you could make a video on the Discrete Fourier Transformation and/or the Fast Fourier Transformation.
Thank you so much! I'll be honest, discrete mathematics isn't exactly my forte, but I will probably end up creating at least one video on the topic because I've heard interesting things
Not exactly sure why I watched the entire video, considering I've done all that in depth throughout my academic journey, but damn, that's an easy to grasp and extremely quick explanation to lots of interchanging mathematical concepts that I was taught through years of math classes. Honestly well done. Had this existed half a decade ago, it would have made my life way more "understandable" (definitely not easier - applying everything mentioned here to actual use is why proper education takes years, not 30 minutes).
I love why math works and I’m glad more people are covering it in depth. You should do mechanics next, it’s pretty easy to explain how we get the laws of motion and why things like energy are useful
30:43 thank you man. i feel so validated. i tried explaining to everyone i could that sines and cosines just don't feel usable. un-graspable and undefined. but here they are. in their true form. beautiful.
another way to write sin and cos: sin(z) = (e^(iz) - e^(-iz))/(2i) cos(z) = (e^(iz) + e^(-iz))/2 This format makes them easier to use with complex inputs z, can help you prove derivative and integral trig properties, as well as shows the connection to the hyperbolic trig functions sinh and cosh.
This didn't sit right with me and i kept mentioning it during the stream this was being made I personally would define sin and cos by their infinite taylor series, of course, the formula for the taylor series requires the derivatives of sin and cos respectively, but in the case of sin and cos they're nice infinite sums (for the maclauren series) technically, i think maybe this is a circular definition as the motivation behind taylor series involves the derivatives of sin and cos, and we're using that to define sin and cos, but i can't think of anything better- Defining them in terms of complex exponentiation would require a definition of complex exponentiation If you define complex exponentiation by plugging i into the taylor series of e^x, and then proving e^ix is equal to cos(x)+isin(x), (using the taylor series of cos(x) and sin(x)) you're still using the taylor series. if you don't want to use the taylor series, and just define complex exponentiation by euler's formula, you still have cos and sin in eulers formula! it's a circular definition! Please tell me where i'm wrong- i think i'm probably wrong
@@savazeroa @savazeroa no you're 100% correct, i noticed that in the vid as well that it seemed self-referntial and kinda reduntant but i guess he didn't wanna go on a tangent to explain series but yh defining them with their series expansion would be more correct than what is shown
It was so jarring to be introduced to math like "Divide rise by run DO IT DO IT NOW OR YOU GET BAD GRADE" instead of explaining it more organically like this.
This is math from the 19th century at most, so very much not all of math. The things people are currently doing in math is a lot lot lot more complicated.
I have been struggling with my digital signals and systems course because I was afraid of notation, and I did not completely understand the transition from complex numbers and euler's formula into the Fourier Transform. It's the day before my second midterm, and this video might help me save my grade. Thank you so much, and please make more videos like this to help us engineering students!
As a maths enjoyer, I have no Idea what a normal person would think watching this... But for me, I absolutely love this content! You display it very well.
I love the way you explained trigonometric functions. It really clicks to me now and how they related with imaginary numbers and circles. Peoples like you and your approach to math teaching are helping me a lot to keep up with my collages clases which lacks a lot of depth into the reasoning and logic, sticking only to the exercise resolution aspect of math. Thanks a lot 🙏
That was honestly the most well explained video on maths I have ever seen. My friends often struggle to understand why I find maths so exciting, but I'm pretty sure they'll understand once they watch this. I loved the flow of introducing all of the topics, as well as the animations which made it super easy to not get lost in all of the new words for someone whose first language isn't English. Thank you so much for this wonderful piece of media contributed to the internet, I'll make sure to recommend your channel to as many people as I can.
I've messed with all of these functions and haven't felt like I've ever had a better understanding then right now after watching this video. I'm sure the average person will need more so please keep up the incredible work that you're doing!
@@Snakehandler268 something funny i understood everything in this video and only watched it twice im in 8th grade and my teachers face when i started explaining Fourier transform
Perhaps. But my opinion is that people just aren’t required to, or simply don’t, do enough problems on their own. Math isn’t something you can cram for just before an exam, like, say, history. You need to develop an intrinsic understanding that practically always takes a lot of time, effort and practice.
@chudleyflusher7132 This is true and if you stop using it after high school you will forget things quickly. I had to relearn algebra from the ground up 2 years after I graduated high school cause I took a gap year and solved zero math.
@Snakehandler268 I think, there are the base ideas, and then ideas derived from ideas. Like，when we've had logs in the class, and logs are very easy, even all the laws of logs are easy to remember, but then the teacher asks us to calculate how long it would take a quantum computer to complete an operation, he said you can use logs for that *wink wink* - how tf am I supposed to figure that out on my own?
This is AMAZING. Thank you for making it. I've just finished an AP math course (basic 1st year math in hs ) and this went through and beyond all my knowledge 😅
Then to realize all the math in this video you'll breeze through in your first year if you decide to major in a stem field, like engineering, math or physics.
This was… incredible!! I absolutely love your videos and how you build up concepts. Your visuals are spectacular and your explanations show an amazing and unique ability to communicate concepts in a way that is absolutely perfect for anyone who just feels like “they don’t get it” to have that “aha!” moment.
Top 5 ytbers imo, and remember, aside from Vsauce, this is the only guy that does anything academic in the top 5 I think you have no idea how good ur vids are. Now if you did this with physics THEN I actually straight up explode
This video gave me such a better understanding of trigonometry and its connection to calculus. (I’ve taken up to AP Calculus BC formally). Finding angle measurements is a representation of the where the waves are at a given moment. I finally understand the connection of the unit circle to the waves and calculus. Everything is tied like a bow. Your explanations and transitions are so captivating for a math nerd like myself. I am subscribed and excited to see all your videos!
I've been interested in learning more about the Fourier Transformation and I've seen a lot of videos trying to explain it, but this is probably the first one that is simple enough and yet complete enough to get the required insight to figure how it works. Thank you so much!
You are amazing! Edit: Also, mathematicians are not asking "why is that useful?", because that's for engineers and physicists or computer scientists to figure out. For mathematicians it is entirely enough to say "because we can".
Hi Matik! I've just begun trigonometric, it's hard to approach at the begin, but your video makes me more certainty about mathematic.Great video and greetings from Italy!!!
16:04 well not quite. Because there is no way to get back constants that were lost in the derivative. So we add a constant labeled C to represent them. WARNING‼️:NEVER forget to add constant C!!
Not exactly... In math we cant but If It is a real scenario we can, for exemple imagine a car standing still starts moving we know It acelerating at 4m/s^2 so the intregal in relation to time would be 4t + c = v but the c is the initial velocity wich is 0 so we we know v = 4t (in m/s) so we figured c.
@@everyting9240 well, look at that, you DID add a "c" there. Yes, its 0, but that's the point. You did add it. And also, in all the situations of integration, THAT IS HOW "c" IS FOUND!!! By using constraints, (and pay attention here @everything9240) not just in physics, but in maths too!!!
@@thekiwiflarethey're right though. You often have to solve for the constant using known conditions, and that's a known condition for that case so it's easy to just plug in.
@@FunctionallyLiteratePerson yeah but that completely throws out the point of the original comment - you can't know the initial conditions if all you have is the final result
Excellent video. For the sake of simplicity, we're often taught these topics without any further explanation as to how they were derived and where they were derived from which can leave one with a lot of questions. This video does a great job laying it all out with fun graphics. Subbed!
Bro, this is incredible. The animations, how you explain everything so well and have a great sense of humor. You deserve more attention for your hard work. I wish you well
im going to be super honest with you, this video really opened my eyes to these kinds of mathematical concepts, especially imaginary numbers! seeing things represented like this in such a fun and literal way is exactly the way i think it should be shown! ive maybe just, binge-watched 3 or 4 of your videos and ive got to say, you have huge amounts of potential, and seeing great content like this so underlooked? kinda breaks my heart! keep doing what youre doing!!!!
Exactly and people wonder why people get confused by maths, while people trying to explain it in depth make basic mistakes only to make everything exponentially more difficult within minutes while seemingly trying to beat WPM (words per minte) contest. Leaving people behind from the point basic mistakes were made.
Mate, I really can’t understand how underrated your channel is, I’m mean: great editing, great voice over, a person who clearly know what he’s talking about and most importantly someone that either loves maths and science, (seeing how you’ve uploaded over 600 videos of them), or your really determined to make people understand it to a greater level. I’m a math guy myself but wow, your on another level, I planning to watch more of your videos considering how much effort has been put into them, I can’t even understand how you have such a good upload schedule. My congratulations, you have got a new subscriber and new eyes watching your amazing videos.
This was just a lovely piece of art. I mean the graphics were just unbelievable. Picky question. How long did it take you to create this masterpiece? (And if it has not been obvious, you've gained another subscriber👍)
It’s crazy how bro explains calc before trig, the whole, “sin and cosine just exist because math” is way more simple than “rotating imaginary numbers create wiggly lines that show position on a circle” I’m in calc right now and I really enjoy learning about the proofs and the why’s. My teacher usually leaves that stuff out for simplicity’s sake, which is fine most of my classmates would die trying to watch this video, but it really has helped further my understanding.
16:04 There seems to be a lot wrong with this slide. There's no constant term in the integration. The differentiation also has the differential of y multiplied by f(x) giving the f'(x), instead of differentiation being an operator applied to f(x). Correction: The constant term is explained later in the video, so that is an understandable omission.
This video helped me build my interest back in maths (grabbing my attention back from pc games). Thank you so much ❤ I really appreciate videos like this 🥺 please make more videos in future related to WORLD OF MATHS. Thank you once again 💗
Quick note at 16:00, dy/dx is actually the derivative f’(x) Whereas if we want to do the action of taking the derivative of f(x), We gotta write out d/dx f(x). Think of d/dx as the derivative operator, Just like how x tells us to multiply, d/dx tells us to take the derivative While dy/dx = f’(x)
instant subscribe. Thank you for your very visual kind of approach to math. I've always struggled with learning math with static text book, but understand much more faster with visualization and helps with my imagination of math. Please do more videos like this so us people can learn!
This unironically showed up in my recommended on the perfect moment, cheers from the army, keep up with the good work buddy, really motivated me to learn math just for the love of it!
4:47 Just a minor suggestion. Perhaps avoid the combination of untextured red-green colors in your presentation so they are more color blind friendly. Suggestions: 1. Substituting one with blue or any other color combinations that are color blind friendly 2. Using differentiating textured graphics if you want to keep the red and green. (like the textured bar, columns charts in excel) Hope that helps.
You explained this so well, specifically the trig and calculus parts. It is so abstract for me to look at meaningless numbers and stmbols in the books and homework. Thank you so much!
Thanks for real though I had some misunderstanding in calculus and trigonometry, and you clearly explained them while not making a big deal out of things that can be explained simply. Thank you again and hope you do well. Good luck with your channel and your future works. Peace!
Great video, very satisfying ending, still hate the fact that you wrote sqrt(-1) which is technically undefined and -1^2 = 1^2 forgetting the parenthesis. Love from Brazil 🇫🇷
This may be the most densely packed math video I've seen and I'm an avid watcher of 3b1b but somehow it's also the easiest to understand. Great work dude!
The problem with math is that almost everything builds on top of another, and everything that is proven to be correct only adds to the prior knowledge, nothing correct ever becomes outdated again. Which means you cannot grasp an advanced concept without grasping many more basic concepts first and everything is only expanding more and more. There are a few fields which differ, say basic vector algebra or graph theory where the concepts are not that much related to other fundamental concepts and thus can be learned without prior knowledge of many other things, but this soon changes on advanced levels, when other branches of math are intruding these fields too. Because, the other thing about math is that everything is connected. Having a high degree of variety and a high degree of connection could be a definition of complexity. Thus advanced math inevitably gets complex.
Exactly. If you get lost on one step you're lost for all the following steps. Additionally, notation can be tricky to understand. For example he didn't explain what h means when talking about limits, so every conclusion based on anything using limits doesn't make sense to me. I don't know what f(x) means, I don't know what dx means, and I didn't understand the explanation of the integral sign. Despite "learning" how to differentiate and integrate in school I've never really understood a lot of the notation, which means I've never been able to properly understand or learn anything that builds upon things like these.
@@Porkey_Minch It is a pity that you 'learned' differentiation/integration in school, but don't know the notation. It is hard to imagine how this can be, in fact. But I know these things from myself. Teachers are often not even aware of these things themselves. The integral sign, for instance, is just a sign for 'sum'. It is essentially an old style German 'S' letter. The sum is over a product of the value of a function labeled by the letter f at the variable position x, f(x) in notation, and the infinitesimal (infinitely small) quantity dx, x again denotes the variable, d the differential quantity. It is proven that people, who think of integration as a special kind of summation over some product terms, instead of thinking of calculating an area, for instance, have a much better grasp of the concept outside its usual context of geometry and functions of one variable. The need for a special symbol for summation is just because the summation symbol stands for something discrete, while the integral symbol stands for the same, but continuous. To explain these things, also the history of the notation, takes a few minutes, but can make a huge difference in getting familiar with it.
@@Porkey_MinchThe integral sign is just a compact way of saying “this is a sum of those little rectangles which we make smaller and smaller, then add all of them to get the area under the curve” Same way 3x50 is a compact way of saying “we add the number three 50 times”
24:57 but the term -1² doesnt equal to 1 it equals to -1 because first you square -1 and then multiply it by negative, you should have writed (-1)² which equals to 1
That is the best Video about maths all across the Internet. BY FAR. You can feel the way you are passionate about maths and it is really enlightening. I am studying computersicence since last month and this video really motivated me to keep going.
If I had a nickel for every time MAKiT made a video about the progression of maths I would have four nickels Which is certainly a lot more than the two that Dr Doof had
Bravo! 👏 This is how math becomes easy! Been studying math my entire life and did engineering math throughout college. Also took a graduate level controls class for my master's where we used Fourier transforms, but THIS video right here, has done something none of those classes did. Thanks a lot for posting this. This is golden!
I'm studying mechanical engineering and Analysis (the math we have in the first semester) ends with the Fourier transform and I never really understood it so I never even bothered to learn it cause I could pass the class without it (I know I'll still need it at some point in the future depending what field of mechanical engineering I go into) But this dude really just explained the Fourier transform better than the professors ever did and on top of that made actually want to learn it Huge props!
15:35 The sigma Σ in repeated addition btw does just stand for S as in "sum" (a different word for addition) The Integral symbol ∫ is also just an S. This time from an old way of writing the letter s in cursive (known as the "long s") and again just stands for "sum"
I suggest you watch brain nourishment There's a guy making brainrot videos that talk about math, I don't remember the name, but he's really funny. You can look up one of his videos though (Jenna Ortega teaches u substitution or Taylor Swift explains the Taylor series)
Loved your trig explanation. I’ve understood that sin and cos are respective x and y points on the circle realized over time. I never realized tan is literally just slope equation. Absolutely loved that. THANK YOU SO MUCH for finally explaining the equations for sin and cos. Despite knowing the complex plain and e^i(theta)=…. I never connected it. Never tried to derive it. W video, excited to watch more
Bro i love ur videos so much especially how u use animations and lighting to make it look cleaner, u help me understand math better now i dont hate it, i am just annoyed at it, please if theres anyway i can support u tell me, i don't have money and i ahve already subscribed so i will support in anyway i can.
I have a masters in physics but I've never felt confident in my understanding of maths so I really appreciate how clear and methodical these explanations are. It's a great recap of *why* we do any of this when it's so easy to get bogged down in remembering equations and notation
I never ever intuitively understood the notation for integrals. You've opened my eyes with the "it's just telling you to sum up all rectangles with height f(x) and width dx".
While I haven’t learned anything new from this video, a few years ago my mind would have been blown. I almost learned something like I never knew the name of the variable In the Fourier transform, and I don’t know how to google that symbol. But then you just ignored it. I use math a lot, I commonly use trig in programming and even occasionally calculus with derivatives and antidirivitives. Yet I still watched the video all the way through so you were still entertaining enough, even without me learning anything (though I did just watch most of it on 2x speed) can you tell me the name of that variable, my textbook doesn’t tell me it just shows the symbol.
@@bjornfeuerbacher5514 Actually 🤓🤓 that is a bit unnecessarily pedantic. But if you want to be pedantic then you shouldn't write "xi" either - that is not an official transcription. Anyway it's all explained in detail in the wikipedia link.
@@Simchen What do you mean? As I understand the Wikipedia article, "xi" is the official transcription...? And I wouldn't call it pedantic to distinguish between uppercase and lowercase letters.
“If no real number would work, than how about we just IMAGINE one?” Beautiful transition
Then
wouldnt
Imagine you say?
@georgeoneal8148 IMAGIN IF NINJA GOT A LOWWWW TAPPEEEERRR FAAAAAAAAaaaDDEE
This is a sign to finish my math homework.
Procrastinate to watch MAKiT video
@@MozzarellaWizard FR
Fr same here
It's a _sine_ to finish your math homework.
Same
Thank you. I was explaining to my friend why in "order of operations" that multiplication and division were interchangeable same with addition and subtraction. And when i said "because basically theyre the same thing" she looked at me as if i was crazy 😂
For me things like that help a lot with understanding more complex topics.
They’re the same thing in the sense they’re opposites or inverses of each other, important detail
Bottom line is they commute
The order of operations is an arbitrary convention
@@savazeroa try solving 5+2*6 solely going left to right without using order of operations.
That's how many eggs I collected from the chooks over the past 3 days, so there is a correct answer:
17
Bro just went from addition to a Fourier transform in 40 minutes and made it understandable
One of the best math videos I've ever seen
Couldn’t agree more. If anyone is seeing this and wants to skip because he starts off by describing arithmetic, I urge you to stick around.
I'll get to Fourier Transforms as soon as I finish memorizing 7's multiplication table.
This was a comical account of information packed into one single video... and I'm here for it!
After so, so many streams. It is finally here. The 40min math vid.
I am so glad that Im getting an explanation for complex math, my teachers all basically taught me was "this is how you use them because this is how they are used" but now why they are used that way or what they are, and for me to learn I have to actually understand something at a fundamental level
this is what I'm saying. for real many teachers teach by just saying " this is just how it is" which I think drags out the fun and also much of the basic human crave and understanding of why something is which in return make it easier to learn.
@arqip4767indeed. I agree and some focused on memorisations too much.
3blue1brown does the same
A future original 3B1B in the making, keep up the great work and amazing videos. Would love to see longer videos if it meant minimizing holes and gaps. Thank you for your work!
he's 3b1b but with rgb lol
@@llukaWWW gamer 3b1b
3B1B knows mathematics quite well. This guy doesn't know even basic things.
@@diogeneslaertius3365 what did he sayyyyyyyyyyyyy
@@Shadoxite from my other commentary (only watched a few minutes and stopped): "Tetration is useful in combinatorics and pure mathematics is not about applications.
Applications are easy and they will always show up sooner or later. Root and 1/p power are not the same operations. Only if you match the domains specifically and pick a certain root, you could somewhat bring them together say for R+. They are two very different beasts if you properly consider complex numbers. Why are you confusing people if you don't understand the basics yourself?"
I always find it so odd that people struggle so much with algebra. Probably a result of it being taught way too late, as substitution is so basic that it really should just be taught around the same time as multiplication (and should be followed within a year or two by parentheses and factorisation, as they're another one people tend to struggle with due to how late they're taught.)
Probably failed by american education lol /s
I see people struggling with Fractions, it's so easy, it's literally just division and people struggle with it, in my opinion they should only teach fractions and avoid pure division as much as possible, because in the future(High school) these people won't use "÷" anymore and will only use fraction.
@@reclaimer2019 you could probably teach ÷ when teaching other alternative notations like *, ^, and ↑↑↑ and just teach them like you would alternative characters in English like @, &, etc.
Though you can always just teach both division and fraction notation simultaneously as different was of writing it, as ÷ is really important for factorisation, as 1/x(2+3) [2*(1/x)+3*(1/x)] and 1÷x(2+3) [1÷(2x+3x)] aren't the same thing [x=1, 1/1(2+3)=5, 1÷(2*1+3*1)=1/5]. You Can get around this with 1/(x(2+3)) or a long fraction sign that I don't feel like looking for the unicode for, but a division sign does the job just fine too.
@@reclaimer2019they should be taught that these are equal, also, the notation for a single line equation can get very messy, but it makes absurd sense.
Like how 1/1+1 is different than 1/(1+1), but some people seem to not be able to recognize this.
People struggle with algebra due to the fact it makes no sense. This is because algebra in Western countries isn't taught systematically but with an adhoc approach. When we were going over equations we never went over what operations you can do to them.
Also parentheses aren't explained well usually. For example something like this 5+(5-4) would be "incorrect" to solve as 5+5-4=6 even though the parenthesis in this case do nothing.
when i saw the thumbnail i was like "pshhhhh, math isn't difficult" but then when i pressed the video and saw the first equation i said "nvm"
Not really, it's just notation here. Fourier Transform isn't so hard to understand.
@@virtueose The Laplace Transform? Yeah.
@@SbF6H the thing with these equations is that, if you dont know what it represents, its very difficult to reverse engineer what it represents even if you know the notation unlike some simpler equations. i personally didnt know it but its pretty easy to understand.
fourier, laplace generalizes to all complex values of frequency, fourier only generalizes to those with 0 real component @@SbF6H
@@badabing3391 What do you mean? I was just shoving in real values into FFT and getting my work done perfectly.
"Moles are not a unit!!"
Dude I felt that to my core I absolutely despised conversions 😂😂😂
Got to hand it to you mate, although i knew these concepts beforehand, the visualization and most importantly your explanations were amazing, very underrated video, amazingly put
Merry Christmas! I'm a freshman taking AP CSP and this helped me a lot. I have no prior experience in calculus, so this really helped me get a grasp on frequency space to time space conversions and vice versa. It would be incredibly helpful if you could make a video on the Discrete Fourier Transformation and/or the Fast Fourier Transformation.
Thank you so much!
I'll be honest, discrete mathematics isn't exactly my forte, but I will probably end up creating at least one video on the topic because I've heard interesting things
I love these videos! Also 25:01 I recommend you enclose the -1 in parentheses or else it is -(1)^2 = -1
i was looking for this comment😋
Not exactly sure why I watched the entire video, considering I've done all that in depth throughout my academic journey, but damn, that's an easy to grasp and extremely quick explanation to lots of interchanging mathematical concepts that I was taught through years of math classes. Honestly well done. Had this existed half a decade ago, it would have made my life way more "understandable" (definitely not easier - applying everything mentioned here to actual use is why proper education takes years, not 30 minutes).
Would have liked a bit of a deeper dive into Polar coordinates though, considering how useful they are throughout disciplines.
"\left(
ight)" so your parenthesis stretch to the height of the thing inside
Also \sin \cos and so on to make those operators not cursive
\left(\! \!
ight)
if the space between the interior expression and each parenthesis is too wide
\qty from physics library is good alternative for \left
ight
also usually \mathrm{d} is used for derivatives
@@okicek3016 That's not cursive, it's italics.
I love why math works and I’m glad more people are covering it in depth. You should do mechanics next, it’s pretty easy to explain how we get the laws of motion and why things like energy are useful
yea that should be fun to watch
Mechanics would be sweeeet!!!
YESS!! Mechanics would be a fun video!
derivatives came way earlier than I thought they would
There was a lot of maths to fit into 40 mins (and yet it still took me 4 mins to explain division)
30:43 thank you man. i feel so validated. i tried explaining to everyone i could that sines and cosines just don't feel usable. un-graspable and undefined. but here they are. in their true form. beautiful.
another way to write sin and cos:
sin(z) = (e^(iz) - e^(-iz))/(2i)
cos(z) = (e^(iz) + e^(-iz))/2
This format makes them easier to use with complex inputs z, can help you prove derivative and integral trig properties, as well as shows the connection to the hyperbolic trig functions sinh and cosh.
This didn't sit right with me and i kept mentioning it during the stream this was being made
I personally would define sin and cos by their infinite taylor series,
of course, the formula for the taylor series requires the derivatives of sin and cos respectively, but in the case of sin and cos they're nice infinite sums (for the maclauren series)
technically, i think maybe this is a circular definition as the motivation behind taylor series involves the derivatives of sin and cos, and we're using that to define sin and cos, but i can't think of anything better-
Defining them in terms of complex exponentiation would require a definition of complex exponentiation
If you define complex exponentiation by plugging i into the taylor series of e^x, and then proving e^ix is equal to cos(x)+isin(x),
(using the taylor series of cos(x) and sin(x))
you're still using the taylor series.
if you don't want to use the taylor series, and just define complex exponentiation by euler's formula, you still have cos and sin in eulers formula! it's a circular definition!
Please tell me where i'm wrong- i think i'm probably wrong
@@savazeroa @savazeroa no you're 100% correct, i noticed that in the vid as well that it seemed self-referntial and kinda reduntant but i guess he didn't wanna go on a tangent to explain series but yh defining them with their series expansion would be more correct than what is shown
It was so jarring to be introduced to math like "Divide rise by run DO IT DO IT NOW OR YOU GET BAD GRADE" instead of explaining it more organically like this.
They really make a bad reputation for math. 😢, mathematics in the past explains it patiently.
This video was amazing!! It’s like you distilled all of math and TH-cam to a 40 minute thesis. It was well worth the effort in my opinion.
A lot of math is missing from this, continue to explore!
Oh my friend you have much to explore, it will be the most fucked up, most beautiful endeavor you could ever peer into. Have fun!
This is math from the 19th century at most, so very much not all of math. The things people are currently doing in math is a lot lot lot more complicated.
I have been struggling with my digital signals and systems course because I was afraid of notation, and I did not completely understand the transition from complex numbers and euler's formula into the Fourier Transform. It's the day before my second midterm, and this video might help me save my grade. Thank you so much, and please make more videos like this to help us engineering students!
Thought I was just watching this for funsies. *Sweets in 1st yr engineering*
Im finishing my thesis for my undergrad in physics. Never seen such a beautiful explanation for the Fourier transform.
Amazing vid. :)
As a maths enjoyer, I have no Idea what a normal person would think watching this...
But for me, I absolutely love this content! You display it very well.
As a student in im2h, I got lost 3 minutes before i appears
In Finland normal person should understand this in age of 16-18!
I love the way you explained trigonometric functions. It really clicks to me now and how they related with imaginary numbers and circles. Peoples like you and your approach to math teaching are helping me a lot to keep up with my collages clases which lacks a lot of depth into the reasoning and logic, sticking only to the exercise resolution aspect of math. Thanks a lot 🙏
That was honestly the most well explained video on maths I have ever seen. My friends often struggle to understand why I find maths so exciting, but I'm pretty sure they'll understand once they watch this. I loved the flow of introducing all of the topics, as well as the animations which made it super easy to not get lost in all of the new words for someone whose first language isn't English. Thank you so much for this wonderful piece of media contributed to the internet, I'll make sure to recommend your channel to as many people as I can.
I've messed with all of these functions and haven't felt like I've ever had a better understanding then right now after watching this video. I'm sure the average person will need more so please keep up the incredible work that you're doing!
The problem is that math is explained to fast. Teachers move on to the next subject before the previous one is understood.
In some cases, i feel like math is too easy, like log, I would understand it in 6th grade, alongside with exponents, and log is taught in 10th grade.
@@Snakehandler268 something funny i understood everything in this video and only watched it twice im in 8th grade and my teachers face when i started explaining Fourier transform
Perhaps. But my opinion is that people just aren’t required to, or simply don’t, do enough problems on their own. Math isn’t something you can cram for just before an exam, like, say, history. You need to develop an intrinsic understanding that practically always takes a lot of time, effort and practice.
@chudleyflusher7132 This is true and if you stop using it after high school you will forget things quickly. I had to relearn algebra from the ground up 2 years after I graduated high school cause I took a gap year and solved zero math.
@Snakehandler268 I think, there are the base ideas, and then ideas derived from ideas. Like，when we've had logs in the class, and logs are very easy, even all the laws of logs are easy to remember, but then the teacher asks us to calculate how long it would take a quantum computer to complete an operation, he said you can use logs for that *wink wink* - how tf am I supposed to figure that out on my own?
This is AMAZING. Thank you for making it. I've just finished an AP math course (basic 1st year math in hs ) and this went through and beyond all my knowledge 😅
This is the simplified visual explanation I needed during math classes. THANK you!
you lost me at 0:28
I learned that at 3 years old bro
Ewolkmind
@@fabriziogabrielmartinezval5458YA BRO COME ON WASUP WITH DIS DUDE
Bros one 💀
😂😂😭
The phrase "This is simple" made me entirely give up on math and the sciences as a whole.
This gives it a little more hope lol.
Then to realize all the math in this video you'll breeze through in your first year if you decide to major in a stem field, like engineering, math or physics.
This was… incredible!! I absolutely love your videos and how you build up concepts. Your visuals are spectacular and your explanations show an amazing and unique ability to communicate concepts in a way that is absolutely perfect for anyone who just feels like “they don’t get it” to have that “aha!” moment.
The narrator and the editor deserves an award
Thank you
The intuition for the Fourier transform was really satisfying.
Your comment made me actually watch that bit of the video and wow! What an amazing intuition.
Top 5 ytbers imo, and remember, aside from Vsauce, this is the only guy that does anything academic in the top 5
I think you have no idea how good ur vids are. Now if you did this with physics THEN I actually straight up explode
I am planning on MAKiNG "How Physics Becomes Difficult" and "How Chemistry Becomes Difficult"
@@MAKiTHappen YES YES YES YES YES YES YES
This video gave me such a better understanding of trigonometry and its connection to calculus. (I’ve taken up to AP Calculus BC formally). Finding angle measurements is a representation of the where the waves are at a given moment. I finally understand the connection of the unit circle to the waves and calculus. Everything is tied like a bow.
Your explanations and transitions are so captivating for a math nerd like myself. I am subscribed and excited to see all your videos!
Bro really taught math to an alien
I've been interested in learning more about the Fourier Transformation and I've seen a lot of videos trying to explain it, but this is probably the first one that is simple enough and yet complete enough to get the required insight to figure how it works. Thank you so much!
You are amazing!
Edit: Also, mathematicians are not asking "why is that useful?", because that's for engineers and physicists or computer scientists to figure out. For mathematicians it is entirely enough to say "because we can".
Hi Matik! I've just begun trigonometric, it's hard to approach at the begin, but your video makes me more certainty about mathematic.Great video and greetings from Italy!!!
16:04 well not quite. Because there is no way to get back constants that were lost in the derivative. So we add a constant labeled C to represent them.
WARNING‼️:NEVER forget to add constant C!!
Not exactly... In math we cant but If It is a real scenario we can, for exemple imagine a car standing still starts moving we know It acelerating at 4m/s^2 so the intregal in relation to time would be 4t + c = v but the c is the initial velocity wich is 0 so we we know v = 4t (in m/s) so we figured c.
@@everyting9240 that's physics
@@everyting9240 well, look at that, you DID add a "c" there. Yes, its 0, but that's the point. You did add it. And also, in all the situations of integration, THAT IS HOW "c" IS FOUND!!! By using constraints, (and pay attention here @everything9240) not just in physics, but in maths too!!!
@@thekiwiflarethey're right though. You often have to solve for the constant using known conditions, and that's a known condition for that case so it's easy to just plug in.
@@FunctionallyLiteratePerson yeah but that completely throws out the point of the original comment - you can't know the initial conditions if all you have is the final result
8 minutes in and we're already at derivatives, which took school more than a decade to get to. love it :^)
20:27LMAOOOO "we'll stick to radians because they are just so RAD"😂😂😂😂😂😂😂 im dying of laughters
wasn't that funny tbh
Enviable comedy bar
Excellent video. For the sake of simplicity, we're often taught these topics without any further explanation as to how they were derived and where they were derived from which can leave one with a lot of questions. This video does a great job laying it all out with fun graphics. Subbed!
It seems like bro wanted to flex his maths skills in front of us and he did a really good job
Bro, this is incredible. The animations, how you explain everything so well and have a great sense of humor. You deserve more attention for your hard work. I wish you well
for a lack of better word, this channel is criminally underrated.
Please more math content, your style of explaining mathematical concepts is amazing
Linear algebra explained in a step-by-step fashion would be amazing.
im going to be super honest with you, this video really opened my eyes to these kinds of mathematical concepts, especially imaginary numbers! seeing things represented like this in such a fun and literal way is exactly the way i think it should be shown! ive maybe just, binge-watched 3 or 4 of your videos and ive got to say, you have huge amounts of potential, and seeing great content like this so underlooked? kinda breaks my heart! keep doing what youre doing!!!!
0:57 yes you can. You can imagine the number on the y axis repeated as many times as however big the number on the x axis is and vice versa
Exactly and people wonder why people get confused by maths, while people trying to explain it in depth make basic mistakes only to make everything exponentially more difficult within minutes while seemingly trying to beat WPM (words per minte) contest. Leaving people behind from the point basic mistakes were made.
Yeah but how do you repeat a number 2.2 times though?
@@IndianGeek5589 you repeat it 2.2 times
@@tombullish3198 wait you understood what I meant? Great, I thought I was kinda babbling but I’m happy u understand bro😁
@ yeah but how do you represent the number 4, 2.2 times, without using multiplication.
Mate, I really can’t understand how underrated your channel is, I’m mean: great editing, great voice over, a person who clearly know what he’s talking about and most importantly someone that either loves maths and science, (seeing how you’ve uploaded over 600 videos of them), or your really determined to make people understand it to a greater level.
I’m a math guy myself but wow, your on another level, I planning to watch more of your videos considering how much effort has been put into them, I can’t even understand how you have such a good upload schedule.
My congratulations, you have got a new subscriber and new eyes watching your amazing videos.
This was just a lovely piece of art. I mean the graphics were just unbelievable.
Picky question. How long did it take you to create this masterpiece? (And if it has not been obvious, you've gained another subscriber👍)
3 weeks in total. Around 200-300 hours of work
@@MAKiTHappenthats crazy thanks for the video. Your ability to simplify complex topics is amazing
@@MAKiTHappenrespect
@MAKiTHappen it's Blender? When do you sleep?
It’s crazy how bro explains calc before trig, the whole, “sin and cosine just exist because math” is way more simple than “rotating imaginary numbers create wiggly lines that show position on a circle” I’m in calc right now and I really enjoy learning about the proofs and the why’s. My teacher usually leaves that stuff out for simplicity’s sake, which is fine most of my classmates would die trying to watch this video, but it really has helped further my understanding.
16:04 There seems to be a lot wrong with this slide. There's no constant term in the integration. The differentiation also has the differential of y multiplied by f(x) giving the f'(x), instead of differentiation being an operator applied to f(x).
Correction: The constant term is explained later in the video, so that is an understandable omission.
This video helped me build my interest back in maths (grabbing my attention back from pc games). Thank you so much ❤ I really appreciate videos like this 🥺 please make more videos in future related to WORLD OF MATHS. Thank you once again 💗
1:45 freaked me out wth
Me too bruh wtf
Hey, this was an amazing video that explained mathematical topics in a very approachable manner!
Just wanted to drop by and show support.
23:45 god help you if it’s your first time lmao
I'm a year 10 student in the UK and this is actually a simplified explanation with good animation. Good work.
Quick note at 16:00,
dy/dx is actually the derivative f’(x)
Whereas if we want to do the action of taking the derivative of f(x),
We gotta write out d/dx f(x).
Think of d/dx as the derivative operator,
Just like how x tells us to multiply,
d/dx tells us to take the derivative
While dy/dx = f’(x)
d(f(x)) /dx=f'(x) =dy/dx
instant subscribe. Thank you for your very visual kind of approach to math. I've always struggled with learning math with static text book, but understand much more faster with visualization and helps with my imagination of math. Please do more videos like this so us people can learn!
This is the best math video I’ve ever seen
This unironically showed up in my recommended on the perfect moment, cheers from the army, keep up with the good work buddy, really motivated me to learn math just for the love of it!
4:47 Just a minor suggestion. Perhaps avoid the combination of untextured red-green colors in your presentation so they are more color blind friendly. Suggestions:
1. Substituting one with blue or any other color combinations that are color blind friendly
2. Using differentiating textured graphics if you want to keep the red and green. (like the textured bar, columns charts in excel)
Hope that helps.
Why?
@@xinpingdonohoe3978Because some people are colour blind.
Most colourblind people cant distinguish red and green@@xinpingdonohoe3978
You explained this so well, specifically the trig and calculus parts. It is so abstract for me to look at meaningless numbers and stmbols in the books and homework. Thank you so much!
15:58 The notation is not quite right. dy/dx is a derivative, but derivative of f(x) is d/dx f(x).
yeah dy/dx is implicit differentiation 🤦
differentiate y with respects to x treating y as a function of x
Came to the comments to comment this. Thanks for the good work.
No it was a typo.
He wrote dy/dx f(x) which means we're differentiating y with respect to x and then multiplying it with f(x).
@@powercables
@@rnd_penguin yes, if there is a y, it is multiplication but not differentiating f(x).
Thanks for real though I had some misunderstanding in calculus and trigonometry, and you clearly explained them while not making a big deal out of things that can be explained simply. Thank you again and hope you do well. Good luck with your channel and your future works. Peace!
Great video, very satisfying ending, still hate the fact that you wrote sqrt(-1) which is technically undefined and -1^2 = 1^2 forgetting the parenthesis.
Love from Brazil 🇫🇷
I really appreciate this as it puts it in terms that connects and makes it easier to comprehend. A-levels look easier with this videl man.
bro thinks we wouldn't notice the rad joke
Your amazing! This has been a great watch start till end. We all appreciate the time taken to make the animations too
24:59 supposed to be (-1)^2 = 1. Great video !
yea
i swear my mind was panicking when i didn't see the parenthesis.
This may be the most densely packed math video I've seen and I'm an avid watcher of 3b1b but somehow it's also the easiest to understand. Great work dude!
The problem with math is that almost everything builds on top of another, and everything that is proven to be correct only adds to the prior knowledge, nothing correct ever becomes outdated again. Which means you cannot grasp an advanced concept without grasping many more basic concepts first and everything is only expanding more and more. There are a few fields which differ, say basic vector algebra or graph theory where the concepts are not that much related to other fundamental concepts and thus can be learned without prior knowledge of many other things, but this soon changes on advanced levels, when other branches of math are intruding these fields too. Because, the other thing about math is that everything is connected. Having a high degree of variety and a high degree of connection could be a definition of complexity. Thus advanced math inevitably gets complex.
Exactly. If you get lost on one step you're lost for all the following steps.
Additionally, notation can be tricky to understand. For example he didn't explain what h means when talking about limits, so every conclusion based on anything using limits doesn't make sense to me. I don't know what f(x) means, I don't know what dx means, and I didn't understand the explanation of the integral sign. Despite "learning" how to differentiate and integrate in school I've never really understood a lot of the notation, which means I've never been able to properly understand or learn anything that builds upon things like these.
@@Porkey_Minch It is a pity that you 'learned' differentiation/integration in school, but don't know the notation. It is hard to imagine how this can be, in fact. But I know these things from myself. Teachers are often not even aware of these things themselves. The integral sign, for instance, is just a sign for 'sum'. It is essentially an old style German 'S' letter. The sum is over a product of the value of a function labeled by the letter f at the variable position x, f(x) in notation, and the infinitesimal (infinitely small) quantity dx, x again denotes the variable, d the differential quantity. It is proven that people, who think of integration as a special kind of summation over some product terms, instead of thinking of calculating an area, for instance, have a much better grasp of the concept outside its usual context of geometry and functions of one variable. The need for a special symbol for summation is just because the summation symbol stands for something discrete, while the integral symbol stands for the same, but continuous. To explain these things, also the history of the notation, takes a few minutes, but can make a huge difference in getting familiar with it.
@@Porkey_MinchThe integral sign is just a compact way of saying “this is a sum of those little rectangles which we make smaller and smaller, then add all of them to get the area under the curve”
Same way 3x50 is a compact way of saying “we add the number three 50 times”
Makit, you make me fall in love with maths, physics and everything related to it more and more by every and each video.
24:57 but the term -1² doesnt equal to 1 it equals to -1 because first you square -1 and then multiply it by negative, you should have writed (-1)² which equals to 1
Booo nerd
That is the best Video about maths all across the Internet. BY FAR. You can feel the way you are passionate about maths and it is really enlightening. I am studying computersicence since last month and this video really motivated me to keep going.
If I had a nickel for every time MAKiT made a video about the progression of maths I would have four nickels
Which is certainly a lot more than the two that Dr Doof had
Bravo! 👏 This is how math becomes easy!
Been studying math my entire life and did engineering math throughout college. Also took a graduate level controls class for my master's where we used Fourier transforms, but THIS video right here, has done something none of those classes did.
Thanks a lot for posting this. This is golden!
the two guys chatting in the live chat is more entertaining than the video itself
I'm studying mechanical engineering and Analysis (the math we have in the first semester) ends with the Fourier transform and I never really understood it so I never even bothered to learn it cause I could pass the class without it (I know I'll still need it at some point in the future depending what field of mechanical engineering I go into)
But this dude really just explained the Fourier transform better than the professors ever did and on top of that made actually want to learn it
Huge props!
15:35
The sigma Σ in repeated addition btw does just stand for S as in "sum" (a different word for addition)
The Integral symbol ∫ is also just an S. This time from an old way of writing the letter s in cursive (known as the "long s") and again just stands for "sum"
heh sigma
Your videos are extremely well produced, I love the look of them. I will be using them for my students.
God Bless. Keep up the great work MAKiT
this can fix my brain rot
I suggest you watch brain nourishment
There's a guy making brainrot videos that talk about math, I don't remember the name, but he's really funny. You can look up one of his videos though (Jenna Ortega teaches u substitution or Taylor Swift explains the Taylor series)
Loved your trig explanation. I’ve understood that sin and cos are respective x and y points on the circle realized over time. I never realized tan is literally just slope equation. Absolutely loved that.
THANK YOU SO MUCH for finally explaining the equations for sin and cos. Despite knowing the complex plain and e^i(theta)=…. I never connected it. Never tried to derive it.
W video, excited to watch more
29:44 its okay makit, we dont wnat to put more on your plate
Bro i love ur videos so much especially how u use animations and lighting to make it look cleaner, u help me understand math better now i dont hate it, i am just annoyed at it, please if theres anyway i can support u tell me, i don't have money and i ahve already subscribed so i will support in anyway i can.
16:05 wrong operation, true: d(f(x))/dx = f'(x) , no (dy/dx)*f(x) = f'(x) , what is y in this case??
I have a masters in physics but I've never felt confident in my understanding of maths so I really appreciate how clear and methodical these explanations are. It's a great recap of *why* we do any of this when it's so easy to get bogged down in remembering equations and notation
I never ever intuitively understood the notation for integrals. You've opened my eyes with the "it's just telling you to sum up all rectangles with height f(x) and width dx".
No teacher ever told you that this is the meaning behind the notation?!? :O You had rather bad teachers. :(
@@bjornfeuerbacher5514 Maybe they did, but it was never made clear to me x)
Absolutely loved it!
I can only imagine the amount of hardwork you put into it.
While I haven’t learned anything new from this video, a few years ago my mind would have been blown. I almost learned something like I never knew the name of the variable In the Fourier transform, and I don’t know how to google that symbol. But then you just ignored it. I use math a lot, I commonly use trig in programming and even occasionally calculus with derivatives and antidirivitives. Yet I still watched the video all the way through so you were still entertaining enough, even without me learning anything (though I did just watch most of it on 2x speed) can you tell me the name of that variable, my textbook doesn’t tell me it just shows the symbol.
You mean ξ ? That's Xi.
en.wikipedia.org/wiki/Xi_(letter)
@@Simchen Actually, it's xi.
Xi (uppercase) is Ξ.
@@bjornfeuerbacher5514 Actually 🤓🤓
that is a bit unnecessarily pedantic. But if you want to be pedantic then you shouldn't write "xi" either - that is not an official transcription.
Anyway it's all explained in detail in the wikipedia link.
@@Simchen What do you mean? As I understand the Wikipedia article, "xi" is the official transcription...?
And I wouldn't call it pedantic to distinguish between uppercase and lowercase letters.
It can be any variable you want, but common practice is xi as pointed out here
what a FANTASIC video! Clearly explained and gorgeous visuals, making something that seemed impossible, possible. Thank you
2:36 Shouldn't this be ^a and not ^b?
Awesome work on this one! Exactly what I needed to push harder in my studies. Keep up the good work! Your videos are legendary.
Watching this video and not completely wrapping my head around is like looking at a post game area in a game which you can't reach yet
Alternative Title: "Man explains why math is actually super easy for 40 minutes"
This is why I love math
I always just learnt it because they said it. I watched this video and everything makes sense now, crazy how much a video can teach you! Thx